auflegen
to hang up
To end a phone call by placing the receiver back on the cradle or pressing the corresponding button.
Er wurde wütend und hat einfach aufgelegt.
He got angry and simply hung up.

to hang up / put on / launch
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to hang up
To end a phone call by placing the receiver back on the cradle or pressing the corresponding button.
Er wurde wütend und hat einfach aufgelegt.
He got angry and simply hung up.

'Auflegen' is a separable verb. The prefix 'auf' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der DJ legt gleich seine besten Platten auf.
The DJ is about to put on his best records.
The meaning of 'auflegen' depends strongly on the object. The context makes clear whether you are ending a phone call, working as a DJ, launching a program, or putting something onto a surface.
Er legte wütend auf.
He hung up angrily.
In the meaning 'ein Telefongespräch beenden' (to end a phone call), 'auflegen' is often used without an object when it is clear from context that it is about a phone call.
Sprich lauter, leg noch nicht auf!
Speak louder, don't hang up yet!
When someone 'auflegt' (DJs), in the context of parties or clubs, it means that this person is playing music as a DJ. This meaning is rather colloquial.
Am Freitag legt eine bekannte DJane aus Berlin auf.
On Friday, a well-known female DJ from Berlin is DJing.
In a more formal, often economic or political context, 'auflegen' means to initiate something. Typical objects are 'ein Programm' (a program), 'einen Fonds' (a fund), or 'eine Anleihe' (a bond).
Die Bank hat einen neuen Fonds für nachhaltige Investitionen aufgelegt.
The bank has launched a new fund for sustainable investments.
In connection with cosmetics, 'auflegen' means the same as 'auftragen' (to apply). It is often used for powder, blush, or lipstick.
Sie legte vor dem Spiegel noch schnell etwas Puder auf.
She quickly applied a little powder in front of the mirror.
to play
'spielen' and 'auflegen' can both have to do with music. 'spielen' is used when someone plays an instrument or makes music in general. 'auflegen' is especially used for DJs: they choose music and play it at a party, in a club, or on the radio. A guitarist 'spielt Gitarre' (plays guitar), but a DJ 'legt Musik auf' (DJs / plays music as a DJ). So 'auflegen' is more specific when it comes to DJ music.

Am Samstag legt eine DJane im Jugendzentrum auf.
On Saturday, a female DJ is DJing at the youth center.
Mehmet spielt seit zwei Jahren Klavier.
Mehmet has been playing piano for two years.